France responded and nearly found the net through Gauvin soon after, but her back-heel from Kadidiatou Diani did not have enough power to beat Ingrid Hjelmseth.
Kim Do-yeon scored an unfortunate own goal in the 29th minute to give the African champions the lead before Barcelona star Asisat Oshoala, doubled lead in the 75th minute.
However, France secured the win after Eugenie le Sommer converted a penalty with with 18 minutes remaining to secure top spot in the group.
The Koreans, beaten 4-0 by hosts France in the tournament opener on Saturday (AEST), are all but out of contention after a surprise setback in their second Group A game.
There was, though, a lengthy review by the Video Assistant Referee to check on what looked a close handball call against the Nigeria captain as the ball flew past her on the way towards the empty net.
Nigeria inched towards qualifying for the knockout stages of the Women's World Cup for the first time in 20 years after beating South Korea 2-0 on Wednesday.
China and South Africa, who play each other on Thursday, have no points. But after a while we just chose to go for it.
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